Question : The value of $\frac{\cos65^\circ}{\sin25^\circ}+\frac{\cos55^\circ}{\sin35^\circ}-\tan50^\circ\cot50^\circ$ is equal to:
Option 1: 2
Option 2: 0
Option 3: –1
Option 4: 1
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Correct Answer: 1
Solution :
Given:
$\frac{\cos65^\circ}{\sin25^\circ}+\frac{\cos55^\circ}{\sin35^\circ}-\tan50^\circ\cot50^\circ$
= $\frac{\cos65^\circ}{\sin(90^\circ-65^\circ)}+\frac{\cos55^\circ}{\sin(90^\circ-55^\circ)}-\tan50^\circ\frac{1}{\tan50^\circ}$
= $\frac{\cos65^\circ}{\cos65^\circ}+\frac{\cos55^\circ}{\cos55^\circ}-1$
= $1+1-1$
= $1$
Hence, the correct answer is 1.
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